Please give me a complete and clean solution. Find an equation of the hyperbola with center at the origin, a vertex at V (8, 0), and asymptotes with equations 2x ± 4y = 0. Sketch the graph of the hyperbola.

Please give me a complete and clean solution. Find an equation of the hyperbola with center at the origin, a vertex at V (8, 0), and asymptotes with equations 2x ± 4y = 0. Sketch the graph of the hyperbola.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.3: Hyperbolas

Problem 31E

See similar textbooks

Related questions

Q: 1 Find an equation of the hyperbola having foci at (3, –3 – /45) and (3, -3+/45) and asymptotes at y…

A: This question is related to conic section.

Q: Find an equation for the hyperbola that satisfies the given conditions. Vertices: (0, +9),…

Q: Find an equation for the hyperbola whose graph is below. The standard form of the equation is Ay

A: NOTE: Refresh your page if you can't see any equations. . the standard form of the left-right…

Q: I. Find the equation in standard form of the specified hyperbola given the following conditions.

Q: ind of an equation of a hyperbola in the form x2 / M

A: Given that: Centre of the hyperbola = Origin=(0, 0)Length of…

Q: Find an equation of the hyperbola that has foci at (0, -6) and (0, 6), and asymptotes y=x and y=-x.…

A: We will solve the problem

Q: Find the equation of the hyperbola with the following properties. Express your answer in standard…

A: Given:- Foci at (6,-4) and (6.6) Asymptotes of y - 1 = ±(3/4)(x - 6) To find:- Find standard…

Q: Find the standard form of the equation of the hyperbola with the given characteristics and center at…

A: equation of hyperbola if vertices (0, plus minus a) is y2/a2 + x2/b2 = 1

Q: Sketch the hyperbola 9x² – 4y² – 18x + 8y – 31 = 0, and label the center, foci and vertices. Find…

A: Given : 9x2-4y2-18x+8y-31=0

Q: Foci at (0,5) and (0,-5) and a vertex at (0,4)

A: Vertex is at (0,4) Focus is at (0,5) and (0,-5) . Its lies on the y axis So its a vertical hyperbola…

Q: Consider the parabola whose vertex us at (2,-1) amd focus at (0,-1). What is the general form of the…

A: Given, The vertex of the parabola = 2, -1 Focus of the parabola = 0,-1 We have to write the general…

Q: Find the standard form of the equation of the hyperbola with the given characteristicS Foci: (0,…

A: The hyperbola has, Foci: 0,±9; asymptotes: y=±3x

Q: Find the standard form of the equation of the hyperbola with the given characteristics. Foci: (+10,…

A: Given

Q: Find the equation of the parabola with focus at (5, 0) and directrix x = −5.

A: Focus lies on x-axis.

Q: Determine the standard form of equation of a hyperbola with foci at (-1,0), (1,0) and one of its…

Q: Find an equation for the hyperbola that satisfies the given conditions. Vertices: (+1, 0),…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Find the center, foci, vertices, and eccentricity of the hyperbola ( y +…

A: y+32225-x-5264=1⇒y--32152-x-5282=1 Now comparing with y-k2a2-x-h2b2=1, we get k=-3, h=5, a=15 &…

Q: Find an equation for the hyperbola that satisfies the given conditions. Vertices: (±1, 0),…

Q: Find an equation for the hyperbola with center C(0,0), foci F(0,±9), and vertices V(0,±7).

A: Plotting the center, foci, vertices on the graph. We can say that the vertical axis is the…

Q: Find the standard form of the equation of the hyperbola with foci (0, ±2) andasymptotes y = ±19x

A: Find the standard form of the equation of the hyperbola with foci (0, ±2) andasymptotes y = ±1/9x

Q: Find an equation of a hyperbola satisfying the given conditions. Vertices at (1,−7) and (1,1);…

A: Given that the Vertices at (1,−7) and (1,1). So the center will be at the midpoint Center=…

Q: What is the equation of the standard hyperbola with vertices at (0, ±a) and foci at (0, ±c)? Choose…

Q: Find the standard form of the equation of a parabola with focus (8,0) and directrix x = -8.

A: Focus is, a, 0=8, 0⇒a=8 Directrix is x=-8.

Q: find the equation of the given hyperbola Vertices (±3, 0) and asymptotes y = ±1/2 x

A: Since the vertices 3,0 and -3,0 have same y-coordinate, hence the hyperbola is horizontal transverse…

Q: Find an equation of the hyperbola that has foci at (0, -10) and (0, 10), and asymptotes y = 1 x and…

A: To find the equation of hyperbola

Q: Find the equation of the asymptotes for the hyperbola (y – 5)2 – (x + 5)2 = 36. a. y = ±x…

A: Asymptotes are the straight lines which tend to touch the curve at infinity.

Q: Find the standard form of the equation of the hyperbola with the Vertices: (-6, 2), (0, 2);…

A: Introduction: The standard equations of the hyperbola are given by,…

Q: Find the equation of a hyperbola whose vertices are (+2,0) and whose foci are (+5,0). x2 A) 4 = 1 21…

Q: Find the standard form equation for a hyperbola with vertices at (0, 3) and (0, – 3) and asymptote y…

Q: Find an equation of the evolute of the hyperbola y=1/x.

A: Given: The equation of hyperbola,

Q: Find an equation of the parabola in standard form with focus at (3,0) and directrix x=-3

Q: Find the standard form of the equation of the hyperbola with the given characteristics. Foci: (+10,…

Q: Find the equation of a hyperbola whose center is at (0,0), one focus at (5,0) and the distance…

Q: Find the equation of Hyperbola using only the following information: Center at (0, 0) Vertices at…

Q: Find an equation for the hyperbola that has its center at the origin and satisfies the given…

A: The standard form of a vertical hyperbola is: (y-k)2a2-(x-h)2b2=1 ...(i)…

Q: The asymptote of the hyperbola given by x²/9- y²/4 = 1 has the equation?

Q: Find an equation for the hyperbola that satisfies the given conditions. Vertices: (+1, 0),…

A: Consider the general form for the asymptotes is, y=k±bax-h Here, the center is (h,k)

Q: *.. .... Find the standard form of the equation of the parabola with the given characteristic(s) and…

Q: Find the equation of the hyperbola that is centered at (0,0), has vertices at (t10,0) and has 6.…

A: Consider the given values. Center=0,0vertices=±10,0y=±65x The gerneral equation of hyperbola with…

Q: Find an equation for the hyperbola that has vertices (±3,0) and asymptotes y=±5x.

A: Given query is to find the equation of the Hyperbola.

Q: Find an equation for the hyperbola that satisfies the given conditions. Vertices: (0, 16),…

Q: Find the standard form of the equation of the hyperbola with the given characteristics. Foci: (−1,…

Q: Find the standard form equation for a hyperbola with vertices at (8, 0) and (– 8, 0) and asymptote 3…

Q: Find an equation for the hyperbola that satisfies the given condition. vertices at (0, +/- 2) and…

A: Explained below

Q: Find the equation for the hyperbola with the vertices at (0,1) and (6,1) and an asymptote 3y + 2x =…

A: We have to find the equation for the hyperbola according to given information.

Q: Find the standard form equation for a hyperbola with vertices at (0, 21) and (U, y = 74 T

A: Given :Vertices : 0, 21 and 0, -21y=74x

Q: Find the standard form equation for a hyperbola with vertices at (6, 0) and (- 6, 0) and asymptote y…

A: The vertices of the hyperbola is: (6, 0) and (-6, 0) The asymptote of the hyperbola is: y=13x

Q: Find a Cartesian equation for the hyperbola centred at (3,0) with x=1 as one equation of the…

Q: Find the standard form of the equation of the hyperbola with the given characteristics. Vertices:…

Question

Please give me a complete and clean solution.

Find an equation of the hyperbola with center at the origin, a vertex
at V (8, 0), and asymptotes with equations 2x ± 4y = 0. Sketch the graph of
the hyperbola.

Expert Solution